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Atrubin's multiplier in Wireworld Modern

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Atrubin's multiplier in Wireworld Modern

Postby Freywa » January 12th, 2019, 5:15 am

On 11 January 2019, I said on the ConwayLife Discord that I was trying to build a binary multiplier. Calcyman told me about Atrubin's multiplier, a real-time systolic multiplier, and mentioned that it had not been implemented in a cellular automaton as far as he knew.

After a sleepless night I constructed a working prototype of the multiplier in my Wireworld Modern CA.
x = 725, y = 153, rule = WireworldModern
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The inputs are initialised in the shift registers at bottom right, LSB first; the clock pulses are provided by the pulse dividers on top of each cell and behind each shift register, so it works at p1024. An initialisation pulse must also be provided to start the computation, which in the given RLE above is 6 × 7 = 42.
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Re: Atrubin's multiplier in Wireworld Modern

Postby Hunting » January 12th, 2019, 8:54 am

Great one!
Almost c/2:
x = 19, y = 10, rule = LifeHistory
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Re: Atrubin's multiplier in Wireworld Modern

Postby calcyman » January 12th, 2019, 11:52 am

Freywa wrote:The inputs are initialised in the shift registers at bottom right, LSB first; the clock pulses are provided by the pulse dividers on top of each cell and behind each shift register, so it works at p1024. An initialisation pulse must also be provided to start the computation, which in the given RLE above is 6 × 7 = 42.


Very impressive!

For those (like me) wondering how to interpret the output, it seems to be:

  • Crank up your Golly step size to 2^10 (set base = 2, exponent = 10).
  • Press 'tab' and see that the output line is unilluminated, giving a LSD of 0;
  • Press 'tab' again and see that the output line is illuminated, giving the next bit as 1;
  • Press 'tab' again and see that the output line is unilluminated, giving the next bit as 0;
  • Press 'tab' again and see that the output line is illuminated, giving the next bit as 1;
  • Press 'tab' again and see that the output line is unilluminated, giving the next bit as 0;
  • Press 'tab' again and see that the output line is illuminated, giving the next bit as 1;
  • Press 'tab' again and see that the output line is unilluminated, giving the next bit as 0;
  • Press 'tab' again and see that the output line is unilluminated, giving the next bit as 0;
  • Press 'tab' again and see that the output line is unilluminated, giving the next bit as 0;

et cetera, giving a binary result of ...000101010 = 42. (If you don't know how to change Golly's step base, instead go to 8^3 and press double-tab instead of tab in the instructions above.)

Similar to how Paul Rendell built 'stack puffers' to make his Turing machine grow unboundedly in each direction, it should be possible -- in a rule supporting universal construction, such as Nobili32 or GoL -- to have an Atrubin multiplier which extends itself unboundedly to the left so as to be able to multiply unboundedly large integers.
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